The use of system requirements and their risks enables software testers to identify more important test cases that can reveal faults associated with risky components. Having identified those test cases, software testers can manage the testing schedule more effectively by running such test cases earlier so that they can fix faults sooner. Some work in this area has been done, but the previous approaches and studies have some limitations, such as an improper use of requirements risks in prioritization and an inadequate evaluation method. To address the limitations, we implemented a new requirements risk-based prioritization technique and evaluated it considering whether the proposed approach can detect faults earlier overall. It can also detect faults associated with risky components earlier. Our results indicate that the proposed approach is effective for detecting faults early and even better for finding faults associated with risky components of the system earlier than the existing techniques.